ATOMIC AND MOLECULAR EFFECTS IN THE VUV SPECTRA OF SOLIDS

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ATOMIC AND MOLECULAR EFFECTS IN THE

VUV SPECTRA OF SOLIDS

B. Sonntag

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C4, suppldment au no 7 , Tome 39, Juillet 1978, page (24-9

ATOMIC AND MOLECULAR

EFFECTS

IN

THE

VUV SPECTRA

OF SOLIDS

B. SONNTAG

11. Institut fiir Experimentalphysik, Universitat Hamburg,

Hamburg, Germany

RCsumC.

-

Les spectres UVL des solides sont souvent la manifestation d'effets atomiques ou moleculaires dont I'importance se reflkte dans l'allure genkrale des spectres et la structure fine des discontinuitks d'absorption en couche interne. Des preuves de I'influence des elements de matrice atomique et molkculaire, de la structure en multiplets et des corrklations klectroniques sont presen- tkes. L'accent est mis sur la vkrification experimentale directe de cette influence fondke sur la compa- raison des spectres de l'atome ou du solide.

Abstract. -The VUV spectra of solids are often dominated by7 atomic or molecular effects, which clearly manifest themselves in the gross features of the spectra and the fine structllre at inner shell excjtation thresholds. Evideng for the influence of atomic and molecular matrlx elements, multiplet-splitting and correlation is presented. Special emphasis is given to the direct experimental verification based on the comparison of atomic and solid state spectra.

1 . Introduction. - The V W spectra of solids are strongly influenced by localized excitations. Therefore the one-electron band model frequently fails to describe the spectra [l-31. The approaches to over- come this difficulty can be grouped in two classes according to their starting points. The first class is based on the one-electron bandstructure. Local interactions are treated with the help of localized orbitals constructed from Bloch-states. The second class starts out with the states of the free atoms or molecules thereby incorporating intraatomic or intramolecular interactions already at the outset. The influence of the surrounding solid is taken into account by perturbation theory. Due to the small extension of core states core excitations only probe the wavefunctions close to the nucleus. Thus for core spectra atomic or molecular effects are expected to prevail and the latter approach promises a more direct insight in the nature of the excitations.

The main perturbations originate from the nearest shells of neighbouring atoms. Therefore cluster calculations capable of handling varying numbers of atoms seem to be ideally suited. Transfered to experimental physics this approach corresponds to synthe- sizing the spectra of the solids from the experimental spectra of the atomic or molecular building blocks. The ideal experiment would start out with the determination of the spectrum of a single atom and then go on by successively adding atoms thus forming larger and larger clusters until the spectrum is identical with the spectrum of the solid. In reality this is not feasible in most cases, though the possibilities of matrix isolation spectroscopy or cluster formation

in jet streams have not been fully exploited. Inspite of these limitations detailed information on the nature of the core excitations has been obtained by comparing the spectra of the solids with the corresponding spectra of the free atoms or molecules.

2. Gross features of inner shell absorption spectra. - Core states (binding energy

>

20 eV) are confined within a narrow region around the nucleus. In the solid the atomic character of these states is preserved because core states of neighbouring atoms don't overlap. Optical transitions from core states only probe the final state within the region of overlap. For final states > 20 eV above threshold the solid state wavefunctions can be approximated by the wavefunctions of the free atom within a small volume around the nucleus of the excited atom and plane waves outside. This means that only the interaction with the nucleus and the electrons of the excited atom has to be taken into account whereas the interactions with the other atoms in the crystal can be negIected. The validity of this approximation becomes clear if we remember that the outgoing electron wave has to be orthogonalized to all occupied states of the surrounding atoms. This can be achieved by representing the atoms by their pseudopotentials. For final states more than 20 eV above threshold the kinetic energy of the electron is large compared to the variations of the pseudopotential which therefore can be replaced by a constant.

This explains why the gross features of the inner- shell absorption spectra of solids for photon energies

>

20 eV above threshold are well reproduced

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'24-10 B. SONNTAG

by an atomic model. It is o ~ v i o u s that this model generally does not hold at threshold, where solid state effects are important, and fails to reproduce the oscillatory behaviour (EXAFS) of the absorption coefficient .of molecules and solids extending far above threshold.

V W absorption spectra of solids show all the features characteristic for the VUV spectra of atoms.

Wide extension of the spectrum.

-

The inner-shell absorption spectra extend far above threshold.

Dominance of the l -t 1

+

1 transitions. - The

oscillator strength of the l + l

+

1 transitions is generally one or two orders of magnitude larger than the oscillator strength of the l -P l

-

1 transi-

tions.

Delayed onset.

-

Often the absorption is suppressed at threshold by a centrifugal barrier. The spectrum reaches its maximum far beyond threshold.

Resonance near threshold. -

If

nl -t nl

+

1 , l 7 1 transitions are allowed within the same shell

giant resonances show up

-

20 eV above threshold. With increasing Z the resonance shifts towards threshold.

Cooper minima.

-

If the initial wave function has nodes i.e. n > 1

+

1, the transition probability for

nl -t el

+

1 transitions goes through zero above threshold.

The features listed above are well reproduced by one-electron models [4]. In these models the oscillator strength f(n1 -+ &l1), averaged over all orientations,

for transitions from an initial state with quantum numbers n, 1 to a final state with kinetic energy E is

given by

where the matrix element

The wavefunction Pn,(r) obeys the radial equation

V(r) represents a realistic atomic potential obtained by selfconsistent-field calculations.

Fi'g'ure

.l

shows the absorption spectra of atomic and solid Ar from threshold up to 500 eV 131. The exceuent'.agreement between both spectra demonstra- tes the validity of the atomic model. Both spectra show the 3p -t ~d resonance at 25 eV, the coop& minimum

at 50 eV arid the subsidiary 3p -t ed maximum at 80 eV.

here‘

is similar agreement betGeen'the spectra

of solid and gaseous Ne, Kr knd Xe [3].

FIG. 1. - Absorption coefficient of solid (solid line) and gaseous Ar (from Ref. [3]).

The absolute photoabsorption cross-sections in the single electron approximation differ considerably, sometimes by an order of magnitude, from the values given by experiment. These calculations give resonance maxima much narrower and at lower energies than found experimentally. These discrepancies have been proven to be due to many-electron correlations. The absorption spectra of the atomic rare gases can be successfully described terms of the random phase approximation with exchange (RPAE) [5]. The fact that atomic and solid state spectra almost coincide proves that the atomic correlation effects are essentially unaltered in the solid. In order to demonstrate that the validity of the atomic approach is not limited to solids bound by weak Van der Waals forces, the CS-4d spectra of atomic CS, CS metal, crystalline and molecular CsCl are presented in figure 2 [G].

M 80 90 100 110 120 130 140 150 160 170 180 PHOTON ENERGY leV)

FIG. 2. - CS 4d absorption of molecular and crystalline CsCl, CS metal and atomic CS. The cross-sections calculated by Amusia [ 5 ]

for the 4d absorption . . . ., for the contributions of the outer shells

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ATOMIC AND MOLECULAR EFFECTS IN THE VUV C4-l l

There is

a

marked similarity between the four spectra. They are all dominated by the giant CS 4d -t ~f resonance peaking

-

30 eV above threshold. Except at threshold the theoretical cross-section for atomic CS obtained by RPAE [5] agrees with the experimental result. Due to the neglect of relaxation effects the theory predicts a higher 4d-threshold energy and a steeper rise of the cross-section above the 4d-threshold than determined experimentally. The simultaneous excitation of one 4d and one 5p electron is responsible for the structures between 92 eV and 102 eV.

Photoelectron energy distributions (PED) from valence bands at a series of energies in the ultraviolet (UPS) and X-ray (XPS) regime often show marked differences in the relative strength of characteristic features, which have been attributed to a strong energy dependence of the dipole matrix element. Since high energy photoemission experiments empha- size the region close to the nucleus the energy dependence of atomic matrix elements can be used as guideline. This approach has. turned out to be very promising. Using the characteristic energy dependence of atomic cross sections for transitions from the outer S, p, d and f states the symmetry character of the valence band state of various compounds has been determined from the tiw dependence of the PEDs [7, 81. The PEDs of MoTe, measured at 21 eV, 35 eV and 1486 eV are presented as an example in figure 3 [9].

FIG. 3. - Photoelectron spectra for cc-MoTe, for several photon energies. Binding energies are with respect to the valence band edge. The partial d - -

-

and p

---.-

emissions are included

(from Ref. [9]).

According to McGovern and Williams 191 the total emission N(E, ho) (E = binding energy) "can be factorized into photon energy independent symmetry projected density of states Np(E), N,,(E) and Aw dependent cross-section factors Cp(ho), C,(hw)

N(E, ha) = CP(ko) Np(E)

+

C,(ho) N,,(E)

.

The upper part of the valence band is formed by the MO 4d states; the lower part is derived from the

Te 5p states. Above the resonance near threshold the Te 5p cross section goes through a Cooper minimum, which is well reflected in the low intensity of the p-band at h o = 30 eV.

3. Molecular effects.

-

We already mentioned that the atomic approach fails to describe the oscillatory behaviour of the cross section frequently detected in the absorption spectra of solids above inner-shell excitation thresholds. These oscillations are clearly to be seen in the 2p spectra of Na, A1 [l01 and Si [I l]. The 2p spectra of atomic [l21 and solid A1 [l01 are presented in figure 4. Above threshold the spectrum

-

I ~ I I I I I ' l ~ n "

-

-vapour

_-

----

solid -- atom ,theory

-

X ) 80 90 NO 110 120 130

photon energy (eV)

FIG. 4. - 2p-absorption of atomic and metallic Al. The spectrum calculated by McGuire [l31 is included (from Ref. [12]).

of atomic A1 shows a gradual rise peaking at

--

105 eV and than a slow decline with increasing photon energy. This spectral behaviour is in agreement with that of the calculated spectrum [l31 and can be attri-

buted to the delayed onset of the 2p -t &d transitions.

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C4-12 B. SONNTAG

of the outgoing atomic wave $a with the waves

backscattered from the neighbouring atoms $,,

The absorption cross-section due to transitions from the initial state $i is given by

The first term squared gives the smoothly varying atomic cross section while the mixed term yields a contribution oscillating as a function of final state energy. In essence this oscillation is due to construc- tive and destructive interference between the outgoing atomic and the backscattered waves at the position of the excited atom. According to Ritsko et al. [l51 it is sufficient to perform the calculations for a small cluster comprising the nearest neighbours of the excited atom. The simplicity of the model applied by these outhers precludes the exact determination of the size of the cluster necessary to reproduce the experimental spectrum. Multiple scattering calculations for clusters of varying size based on realistic pseudopotentials and taking the effect of the core hole into account seem to be very promising for this pur- pose. These calculations are by no means trivial but they offer unique advantages for the treatment of inner-shell excitations. Based on the present knowledge it is safe to assume that the essential features of the spectra are determined by only a few shells of nearest neighbours, and thus can be considered quasi molecular.

For molecular crystals like solid SiF, the molecular origin of the corresponding broad peaks above the Si-2p threshold can be verified experimentally [16]. The broad bands above threshold are present in the spectra of molecular and solid SiF, given in figure 5.

1b I I I I I I I 13 - ---- gaseous SiFb ---- s o l ~ d _- E U ---- gaseous SiFb ---- s o l ~ d ---- gaseous 01 I I I I l I I 1 90 n o 110 120 1x1 140 rso rso no PHOlON E N E R G Y IeVl

FIG. 5. - Si-2p absorption of solid and molecular SiH, and SiF,

(from Ref. [16]).

These bands are ascribed to the modulation gf the transition matrix element caused by the superposition of the outgoing wave and the waves backscattered by the F ligands. The interpretation of the bands in term of resonances localized within the cage formed by the F ligands is equivalent to this [17]. Scattering by the nearest Si neighbours is probably responsible for the weak absorption band at 143 eV in the spectrum of solid SiF,. The appearance of a similar band in the spectrum of solid SiH, supports this assign- ment [l 61. The small scattering amplitude of H explains why the resonances are missing in the spectra of solid and molecular SiH, [16, 181.

4. Structure at inner-shell thresholds.

-

So far we have left out the region close to inner-shell thresholds, where solid state effects dominate in many cases. Van der Waals solids are predestinated for the search for atomic or molecular effects at threshold. Figure 6 shows the absorption of molecular and solid SiH, close to the Si 2p-threshold [16, 181.

101 103 105 107

FIG. 6. - Fine structure at the Si-2p threshold of solid [I61 and molecular SiH, [18].

core to valence state transitions give rise to the broad absorption band between 102.5 eV and 104.5 eV [19, 201. Transitions to s and d symmetric Rydberg states, converging to the series limits at 107.2 eV and 107.8 eV are responsible for the sharp lines above 104 eV. These lines are completely smeared

out in the solid whereas the prominent absorption band is only slightly broadened. A deconvolution of this absorption band shows that the intensity ratio of the 2p3,, -+ 0*(4a1), 2p,,, -+ o*(4a1) transi-

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ATOMlC AND MOLECULAR EFFECTS IN THE VUV C4-13

:

has been successfully applied to the interpretation

I of the structure at inner-shell absorption thresholds

of alkali-halides [21] and to the X-ray emission 1221 and photoemission [22, 231 of transition metal compounds. The strong ionic multiplet splitting is incorporated by taking ionic spin-orbit, Coulomb and exchange interactions into account. The influence of the neighbouring ions is included via the field produced by them at the position of the excited ion. The 4d-spectra of rare-earths metals form the most striking example for the importance of atomic effects at -inner-shell thresholds 124-261. The 4d-absorption of atomic and metallic Ce [27] in the energy range from 100 eV to 150 eV is shown in figure 7. There is

(10 cm-' 1

energy (eV)

FIG. 7. - 4d-absorption of atomic and metallic Ce in the energy range from 100 eV to 150 eV. The calculated spectra

(solid line) and Ce3+ 4d1° 4f 5s2 5p6 + 4d9 4f2 5s2 5p6 (Ref. [29], dashed line) are included (from Ref. [27]).

an excellent agreement between the spectra of both phases. Details of the fine structure at the 4d-threshold of atomic and metallic Ce are given in figure 8. The agreement between the two spectra is almost perfect. The energies of most of the maxima showing up in the spectra of atomic and metallic Ce agree within the experimental errors.

transitions determine the spectrum of atomic Ce. The strong Coulomb (F2(4d, 4f), F4(4d, 4f)) and exchange (G,(4d, 4f), G3(4d, 4f), G5(4d, 4f)) interactions give rise to a multiplet splitting of more than 20 eV. The highest levels, which comprise most

af the oscillator strength are raised above the ioniza-

FIG. 8. - Fine structure at the 4d threshold of atomic and metallic Ce. The calculated spectra

(solid line) and Ce3+ 4d1° 4f Ss2 5p6 + 4d9 4f2 5s2 5p6 (Ref. [29],

multiplied by 0.5, dashed line) are included (from Ref. [27]).

tion limit [28, 291. This is borne out by the results of intermediate coupling calculations [27] of the multiplet splitting and relative oscillator strength for the Ce 4d1° 4f 5s2 5d 6s2('G4) -+ 4d9 4f2 5s2 6s2 transitions to all 3 = 3, 4, 5 final states included in figure 7 and figure 8. To facilitate comparison with the experimental data the 461 lines havebeen convo- luted with a Lorentzian of 0.2 eV halfwidth. The interaction of the highest multiplet levels with the underlying continua gives rise to the giant resonance at 125 eV. The importance of many-electron correlations which are essentially unchanged in the solid is obvious. The rearrangement of the outer 5d and 6s electrons hardly influences the spectra. In addition to the experimental results this is supported by the calculation of the 4d10 4f + 4d9 4f2 transitions of the Ce3' ion 1291.

The interaction between a vacancy in the 4d-shell and the partly filled 4fn shell also manifests itself in the soft X-ray emission spectra of rare-earths [30]. The emission spectra for La, Sm, Gd, Ho and Lu, corrected for bremsstrahlung contribution are shown in figure 9. Electron bombardment of rare-earths with the configuration 4d1° 4fn 5s' 5p6 (outer electrons omitted) can

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C4-14 .B. SONNTAG

FIG. 9. -Soft X-ray emission spectra of La, Sm, Gd, Ho and Lu [30].

ii) transfer a 4d electron to an empty 4f state

Transitions from both states thus created contri- bute to the soft X-ray emission. For 1 n < 14 the multiplet components of these states are spread over

-

20 eV. The multiplet splitting of %,he 4d9 4fn 5s' 5p6 states (case i) causes the complicated structure of the 4d X-ray photoemission spectra [3 l]. Since the 4dy 4fn 5s' 5p6 and the 4d' 4 P f ' 5s2 5p6 multiplets overlap it is difficult to disentangle their contributions to the emission. Zimkima et al. [30] ascribed the emission band A to the transitions

The multiplet splitting is responsible for the conside- rable width of the band. For CS there is no multiplet splitting because of the drastically reduced overlap of the 4d and 4f wave functions. The corresponding

emission band therefore can be resolved into three narrow components due to the N5 + O,, N, -+ O,,

0, transitions. The wide emission band above B has been assigned to two types transitions

i) 4d9 4f" 5s' 5p6 -+ 4d1° 4f"-' 5s' 5p6 ii) 4d9 4fnf1 5s' 5p6 -+ 4d1° 4fn 5s' 5p6.

Because of the high absorption above the 4d threshold part of the structures may be due to self-

absorption though 1,5 keV electrons have been used for excitation. The sharp La emission lines at 97,3 and 101,7 eV exactly coincide with the lowest (La3+ 'S, + 3 ~ 1 , 3 ~ 1 ) 4d absorption lines. This proves that reemission takes place. With increasing Z ,

i.e. filling of the 4f shell, the intensity ratio of the 4d + 4f emission to the 4d -+ 5p emission increases.

For Lu band A is hardly detectable. In contrast to

the spectra of La-Tm the Lu 4d + 4f emission gives

rise to two narrow, well resolved bands, which are separated by the spin-orbit splitting of the 4d,,2,3,2 levels [31]. The 4f shell of Lu is completely filled and therefore there is no multiplet splitting due to the 4d-4f interaction.

Multiplet splitting is also expected to influence the inner-shell spectra of transition metals, though the outer d-states are less localized than the 4f states of the rare earths. The complicated behaviour of the electrical, optical and magnetic properties of transition metals is due to the partly local and partly itinerant character of the outer d-states. At threshold of the 3p-excitation the absorption spectra of the 3d-metals exhibit a strong asymmetric absorption

p h o t o n e n e r g y ( e V )

F'IG. 10. - 3p-absorption of atomic (solid line) and metallic [32]

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ATOMIC AND MOLECULAR EFFECTS IN THE VUV C4-15

band [32-351. The width of this band by far exceeds the width of the empty part of the 3d-band. In analogy to the rare earths this band has been attributed to 3p6 3dn + 3p5 3dn+' (outer electrons emitted) transitions split by the interaction of the partly filled d shell with the 3p-hole. Dietz et al. [34] and Davis and Feldkamp 1351 have shown that the inclusion of a Fano type interference effect between the 3p6 3dn + 3p5 3dn+' and the 3p6 3dn + 3p6 3dn-' E f

transitions is essential, because 3p5 3d"+ l autoionizes

into 3p6 3dn-' cf via super Coster-Kronig transition. Figure 10 shows the 3d-absorption spectra of atomic and metallic Fe, CO and Ni.

The validity of the atomic approach is borne out by the close correspondence between the gross features of the spectra of both phases. Similar results have been obtained for Mn 1361. But in contrast to the

4d spectra of the rare earths there are marked differences between the spectra clearly manifesting the partly itinerant nature of the 3d electrons. The atomic spectra show sharp lines and broad structures which are absent in the spectra of the metals. Part of these structures are reproduced by the calculations per- formed by Davis and Feldkamp [35], but the relative energy positions and oscillator strengths deviate considerably from the experimental results.

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